A load coil is an inductor that is inserted into a circuit to increase its inductance. Load coils are often inserted into a transmission line, e.g., a loop, to reduce amplitude and phase distortions of signals transmitted over the transmission line. As a result of their relatively high inductance, load coils generate poles in the transfer function representing the characteristic impedance of the transmission line.
With reference to FIG. 1, in the past, load coils 110 were inserted periodically, e.g., at a spacing on the order of kilometers, into a twisted-pair transmission line 100 used for plain old telephone service (POTS) to improve the quality of voice signals transmitted over the transmission line 100. Typically, each load coil 110 includes two windings 111, each connected in series with one wire 101 of the twisted-pair transmission line 100.
However, the insertion of load coils into the transmission line leads to a rapid increase in attenuation above a cut-off frequency that depends on the spacing of the load coils. Typically, transmission lines including load coils at a spacing suitable for POTS have a cut-off frequency just above the upper voice frequency limit of 3.4 kHz. Therefore, in order to use these loaded transmission lines for services, e.g., digital subscriber line (DSL) services, operating at higher frequencies, e.g., above 10 kHz, the load coils must be detected and removed.
One prior-art technique for determining the number of load coils in a transmission line involves finding, e.g., by taking a derivative, and counting local maxima in the characteristic impedance of the transmission line. Variations of this technique are disclosed in U.S. Pat. No. 7,778,317 to Jin, issued on Aug. 17, 2010, in U.S. Pat. No. 7,395,162 to Fertner et al., issued on Jul. 1, 2008, in U.S. Pat. No. 5,881,130 to Zhang, issued on Mar. 9, 1999, in U.S. Pat. No. 5,404,388 to Eu, issued on Apr. 4, 1995, and in U.S. Pat. No. 4,087,657 to Peoples, issued on May 2, 1978, for example. Unfortunately, when the local maxima are close to one another or overlapping, it is often difficult to correctly determine the number of local maxima.